- 期刊
FRACTIONAL POWERS OF NON-NEGATIVE OPERATORS IN FRÉCHET SPACES
摘要
In the present paper the theory of fractional powers, which has been restricted to date to certain operators on Banach spaces, is generalized to certain particular operators in Fréchet spaces. The main difficulty consists in the fact that neither the holomorphlc functional calculus nor the results on Banach algebras are available for bounded operators on Fréchet spaces. All the basic properties which a good theory of fractional powers must fulfill are proved, except for the spectral relation, σ(A^α) = {z^α: z∈σ(A)} which remains an unsolved problem.
延伸閱讀
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